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A355521
Primes that cannot be represented as 2*p+q where p, q and (2*p^2+q^2)/3 are prime.
1
2, 3, 5, 7, 13, 31, 37, 97, 211, 271
OFFSET
1,1
COMMENTS
2*p^2+q^2 is always divisible by 3 when neither p nor q is divisible by 3.
Conjecture: there are no other terms.
EXAMPLE
11 is not in the sequence because 11 = 2*2+7 with 2, 7 and (2*2^2+7^2)/3 = 19 prime.
MAPLE
M:= 50000:
Pr:= select(isprime, [2, seq(i, i=5..M, 2)]):
nP:= nops(Pr):
S:= convert(Pr, set) union {3}:
for p in Pr do
if 2*p+2 > M then break fi;
for q in Pr do
r:= 2*p+q;
if r > M then break fi;
if isprime(r) and isprime((2*p^2+q^2)/3) then
S:= S minus {r}
fi
od od:
S;
CROSSREFS
Cf. A355518.
Sequence in context: A067573 A103199 A054217 * A048414 A048399 A249692
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Jul 05 2022
STATUS
approved